The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in Lorenz equations motivates this study. A weak non-linear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the validity condition and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions showing an excellent fit within the validity domain of the analytical solution.
Analytical Prediction of the Transition to Chaos in Lorenz System
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Vadasz, P. "Analytical Prediction of the Transition to Chaos in Lorenz System." Proceedings of the ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. Volume 2: Automotive Systems; Bioengineering and Biomedical Technology; Computational Mechanics; Controls; Dynamical Systems. Haifa, Israel. July 7–9, 2008. pp. 799-803. ASME. https://doi.org/10.1115/ESDA2008-59568
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